scatter plots as 12.4.2
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ScatterScatter
PlotsPlots
A S – 12.4.2
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Scatter plots are used
for data sets in whichthere could to be somesort of patternbetween two different
variables.• Scatter plots are most useful whenthere
are a large number of points. Thesedatapoints are plotted but not joined.
• Points that do not fit the generaltrend isan outlier. Do not consider this pointwhen “looking” at trends.
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Francois records how
many hours his friendsspent studying andthen records whathappens to their
marks.
hoursstudying %change
1 1
1 -12 2
3 1
3 54 3
6 2
5 4
It is not easy to see anypattern or trend.
e.g. one friend studied for1 hour and his markschanged by 1% whileanother friend also
studied for one hour and
An ExampleAn Example
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hours
studying
%
change
1 1
1 -1
2 2
3 1
3 5
4 3
6 3
5 4
Graph this data.
1 2 3 4 5
Study hours
6
5
4
3
2
10
-1
%
change
What does Frans notice?
Points are scattered but they seem to be
getting higher as the number of hoursincrease.
DO NOT connect the dots.
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1 2 3 4 5
Study hours
6
5
4
3
2
10
-1
%
change
This is called the line of best fit – It helpsto show the trend between the variables.
Now draw a
straight line thatruns as close aspossible throughthe middle of
the set of datapoints.
Using this line of best fit, suggestFrans’s % change in his mark if hestudied 2 hours.
1%
Use your ‘eye’ - try to get an equalno. of points on either side.Disregard outliers.
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When a scatter plot shows an associationor trend between two variables there isnot necessarily a cause and effect
relationship. It is only a suggestion as both variablescould be related to some third variablethat actually causes the apparentassociation.
Associations
The relationshipbetween the variablescan be either positive,negative or have no
association.
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Types of ScatterTypes of Scatter
PlotsPlots This plot couldshow anincrease in achild’s height astheir ageincreases.
This plot could
show an increasein a child’s massas their ageincreases.
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Make asuggestion asto what eachscatter plotcould show.
T o d o
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Which graph most likely represents the followin
• The height of boys and the size of shirts worn by them.
• The temperature and the amount of gasneeded
to heat a house on a day.
• The size of shoes of adults
x
y
x x x
xxx
x
Graph A
x
y
x x x
x xx
x
Graph B
x
y
x
x
x
xxx x
Graph C
Graph A
Graph C
Graph B
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TVhours
Grade%
12 70
10 85
5 823 88
15 65
16 75
8 68
A survey of randomly selected learnerscompared the no. of hours of TV they
watchedper week with their grade averages.
Create a scatter plot for thisdata.
100
80
60
40
20
0
TV hours0 4 8 12 16
Gra
de%
Let’s PlotLet’s Plot
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100
80
60
40
20
00 4 8 12 16
Can you make anysuggestions aboutthe effect that
watching TV has onacademicachievement?
Classify the linear association.Draw a line of best fit.
Weak negative
The more TV you watch the greater
the chance of a decrease in
Use this line to determine your grade % if you watch 8 hours of TV.
80 hours
Grad
e%
TV hours
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0 1 2 3 4 5 6 7
90
80
7060
50
40
30
20
10
0Age in year
Price
(R
)i n
thousa
nds
This scatter plotshows the selling
price of secondhand cars of thesame model.One car isadvertised
wrongly. Give theage and price.6 years, R72 000
What type of association is this?Strongly negative
A 4-year old car has to be
advertised. What price should it ≈ R55 000
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A consumer group collected thefollowing data on the relationship
between the mass of a car and itsaverage consumption in ℓ /100km.Mass(kg)
ℓ per100km
1250 5
1420 7,6
950 4,2
1850 61220 6,8
1650 7,2
1010 6
Create a scatter plot for thisdata.
0 400 800 1200 1600 2000
mass(kg)
12
108
6
42
0ℓper
100k
m
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0 400 800 1200 1600 20mass(kg)
ℓ
per1
00k
m
12
10
86
4
2
0
Circle the outlier.
Predict the mass if the car uses8ℓ 100km. 1800kg
What type of association isthis?
Circle the car that
travels the furtheston 50ℓ of petrol.
Strong positive
What does the
graph tell us aboutthe mass of thecar and theconsumption?
The greater the mass, the greater the consumpti
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ww
w.rand
-forex.co.za
Is the Dollar stronger
or weaker if the Dollarper Euro rateincreases?
The scatter plotshows the relationship
between the Dollarper Euro and the goldprice in 2004.
What does the line of best fit tell us about therelationship between the Dollar, Euro and goldprice.
The gold price is increasing while
the dollar is weakening against
Weaker